Is BSc Zoology, BEd, MA History eligible for a PGT History post?

The eligibility criteria for a PGT in History will be
1. A post-graduate degree in the concerned subject. If you want to work as a History PGT. you should have a Master's degree in History.
2. You should complete your B.Ed or M. Ed.

I have not mentioned any other aspects like age and other criteria.

You can do your MA in any recognised university irrespective of regular or distance or open university. If you are doing a regular course also from a university which does not have UGC recognition, you will not be eligible for PGT. So please join a university that is having UGC recognition for the course you are studying.

But I feel you should go for an M.Sc in zoology instead of MA, History so that you will be eligible for both Graduate teacher as well postgraduate teacher. You can do your B.Ed with science specialisation so that you can join as a natural science teacher.

As mentioned above, you are planning to do M.A. in history and B.Ed. So, you are eligible for PGT history because graduation subject is not part of the eligibility criteria. To become PGT history. You should have a master's degree in history with a minimum of 50% in history with B.Ed.degree. Your degree should be UGC recognized. Otherwise, you may disqualify from this post. Another option is, you can do M.SC in zoology. Then you will be eligible for both TGT and PGT. You can do B.Ed with science also. It would be more beneficial for your career point of view.

Your graduation in Zoology is not likely to impact your B.Ed course with the option of History. Moreover you are planning to take up subject History in your post graduation stage.
Hence in no way, it would affect you to become PGT in History.
The School Administration would like to see the same subject in your post graduation and B.Ed course so that they would select you as a Post Graduate Teacher.
Ensure that your both the degrees- B.Ed and M. A. In History are recognised from UGC. Hence it is not necessary that you should take up regular courses only for fulfilling your ambition. Better you take up History in your post graduation stage through the regular mode having its affiliation through UGC apart from taking up B. Ed through the distance mode from a recognised university so that UGC status is maintained. In that way, you would save time while doing the dual degrees.

For applying a position as PGT teacher one has to have postgraduate degree in the particular subject along with B.Ed qualification. So as per your plan you are going to attain the same in due course of time. So there is no problem in that.
It is imperative that you should try to get good grades in all these exams so that when you apply for a PGT teacher you stand in merit and get the position.
One thing which I want to mention in this matter is that whenever there are a large number of candidates applying for a position then the selection committee always see the comparative strength of the candidates. So it is possible that they may give some preference to those who have done same subject in their UG as well as PG course. Though there is no hard and fast rule like that but when comparison of the candidates is done then all these things are kept in mind by the selection committee.
In view of the above point it makes sense to do UG and PG with the same subject to create strength in that academically as well as from getting a job point of view.
Same strategy is to be followed for selecting the subjects in B.Ed course. Today we are living in a world where specialisation is considered a qualification. So concentrating and focusing our academic acquisitions in a particular stream will always be useful and helpful for making a career.